1.0.0 Context and analysis goal(s):
1.1.o Contexts Housing is an essential component of household wealth worldwide. Buying a housing has always been a major investment for most people. The price of housing is affected by many factors. Some of them are global in nature such as the general economy of a country or inflation rate. Others can be more specific to the properties themselves. These factors can be further divided to structural and locational factors. Structural factors are variables related to the property themselves such as the size, fitting, and tenure of the property. Locational factors are variables related to the neighbourhood of the properties such as proximity to childcare centre, public transport service and shopping centre.
Hedonic pricing model is used to examine the effect of housing factors as discussed above on the price. Conventional, this model was built by using Ordinary Least Square (OLS) method. However, this method failed to take into consideration that spatial autocorrelation and spatial heterogeneity exist in geographic data sets such as housing transactions. With the existence of spatial autocorrelation, the OLS estimation of hedonic pricing models could lead to biased, inconsistent, or inefficient results (Anselin 1998). In view of this limitation, Geographical Weighted Regression (GWR) was introduced for calibrating hedonic price model for housing.
1.2.1 Exploratory Spatial Data Analysis
In this take-home exercise, we need to build a hedonic pricing models to explain factors affecting the resale prices of public housing in Singapore. The hedonic price models must be built by using appropriate GWR methods.
- Understanding the Dataset
2.1 Resale flat
Datas: Aspatial + Resale flat prices based on registration date from jan 2017 onwards. + hawker centres + supermarkets Sources: + https://data.gov.sg/dataset/resale-flat-prices + https://www.onemap.gov.sg/docs/
Geospatial + Train Stations: MRTLRTStnPtt.shp + Singapore Planning Subzones: MP14_SUBZONE_WEB_PL.shp
Sources: + http://insideairbnb.com/get-the-data.html + https://cran.r-project.org/web/packages/onemapsgapi/index.html + https://datamall.lta.gov.sg/content/datamall/en/search_datasets.html?searchText=mrt%20stations
- Importing Required Packages
packages = c("maptools","sf","raster","spatstat","tmap","tidyverse", 'sp','olsrr', 'corrplot', 'ggpubr', 'spdep', 'GWmodel','httr','jsonlite','nngeo','stringr')
for(p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}
- Retrieving data from OneMap API
4.1.1 Supermarket
queryName = "supermarkets"
supermarketUrl = paste(c(url,"?queryName=",queryName, "&token=",token),collapse = "")
supermarketUrl
[1] "https://developers.onemap.sg/privateapi/themesvc/retrieveTheme?queryName=supermarkets&token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOjc5NDgsInVzZXJfaWQiOjc5NDgsImVtYWlsIjoianVubG9uZy50b2guMjAxOUBzbXUuZWR1LnNnIiwiZm9yZXZlciI6ZmFsc2UsImlzcyI6Imh0dHA6XC9cL29tMi5kZmUub25lbWFwLnNnXC9hcGlcL3YyXC91c2VyXC9zZXNzaW9uIiwiaWF0IjoxNjM2MjYzNTcwLCJleHAiOjE2MzY2OTU1NzAsIm5iZiI6MTYzNjI2MzU3MCwianRpIjoiNzU4YjQ3NjE3YWYwM2E5NzhjY2RiYmUzMGQ2ZjRlNjcifQ.CW1QqnmI-_0Z_wxwAylq0hOCdTkNsh1Nnin4c2yNR2g"resp = GET(supermarketUrl)
supermarkets = fromJSON(rawToChar(resp$content))
supermarkets = do.call("rbind", supermarkets)
supermarkets = supermarkets[c(6,7,8,9,10,11,12,13)]
supermarkets = supermarkets[-1,]
rownames(supermarkets) = 1:nrow(supermarkets)
glimpse(supermarkets)
Rows: 526
Columns: 8
$ NAME <chr> "LI LI CHENG SUPERMARKET (PUNGGOL) PTE. LTD.", "~
$ DESCRIPTION <chr> "NE12I65N000", "E73010V000", "NE11909C000", "S02~
$ BLK_HOUSE <chr> "273C", "11", "683", "631", "201B", "201D", "421~
$ STR_NAME <chr> "PUNGGOL PLACE", "UPPER BOON KENG ROAD", "HOUGAN~
$ UNIT_NO <chr> "884", "901", "903", "954", "1091", "1161", "116~
$ POSTCODE <chr> "823273", "380011", "530683", "470631", "522201"~
$ LatLng <chr> "1.40230300615945,103.901262393433", "1.31423937~
$ ICON_NAME <chr> "supermarketlogo.jpg", "supermarketlogo.jpg", "s~4.1.2 Hawker Centres
queryName = "hawkercentre"
hawkerCentresUrl = paste(c(url,"?queryName=",queryName, "&token=",token),collapse = "")
hawkerCentresUrl
[1] "https://developers.onemap.sg/privateapi/themesvc/retrieveTheme?queryName=hawkercentre&token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOjc5NDgsInVzZXJfaWQiOjc5NDgsImVtYWlsIjoianVubG9uZy50b2guMjAxOUBzbXUuZWR1LnNnIiwiZm9yZXZlciI6ZmFsc2UsImlzcyI6Imh0dHA6XC9cL29tMi5kZmUub25lbWFwLnNnXC9hcGlcL3YyXC91c2VyXC9zZXNzaW9uIiwiaWF0IjoxNjM2MjYzNTcwLCJleHAiOjE2MzY2OTU1NzAsIm5iZiI6MTYzNjI2MzU3MCwianRpIjoiNzU4YjQ3NjE3YWYwM2E5NzhjY2RiYmUzMGQ2ZjRlNjcifQ.CW1QqnmI-_0Z_wxwAylq0hOCdTkNsh1Nnin4c2yNR2g"resp = GET(hawkerCentresUrl)
hawkerCentres = fromJSON(rawToChar(resp$content))
hawkerCentres = do.call("rbind", hawkerCentres)
hawkerCentres = hawkerCentres[c(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)]
hawkerCentres = hawkerCentres[-1,]
rownames(hawkerCentres) = 1:nrow(hawkerCentres)
glimpse(hawkerCentres)
Rows: 125
Columns: 17
$ NAME <chr> "Bedok Reservoir Road Blk 630",~
$ DESCRIPTION <chr> "HUP Rebuilding", "HUP Standard~
$ ADDRESSBLOCKHOUSENUMBER <chr> "630", "16", "29", "38A", "166"~
$ ADDRESSPOSTALCODE <chr> "470630", "460016", "330029", "~
$ ADDRESSSTREETNAME <chr> "Bedok Reservoir Road", "Bedok ~
$ PHOTOURL <chr> "http://www.nea.gov.sg/images/d~
$ LANDXADDRESSPOINT <chr> "36985", "39376.14", "31305.63"~
$ LANDYADDRESSPOINT <chr> "35039.64", "33645.7", "33497.8~
$ EST_ORIGINAL_COMPLETION_DATE <chr> "30/6/1982", "12/5/1975", "17/3~
$ STATUS <chr> "Existing", "Existing", "Existi~
$ ADDRESSTYPE <chr> "I", "I", "I", "I", "I", "I", "~
$ HUP_COMPLETION_DATE <chr> "28/2/2006", "20/9/2012", "31/1~
$ ADDRESS_MYENV <chr> "Blk 630, Bedok Reservoir Road,~
$ LatLng <chr> "1.33315924777343,103.914053888~
$ ICON_NAME <chr> "HC icons_Opt 8.jpg", "HC icons~
$ APPROXIMATE_GFA <chr> NA, NA, NA, "1733.074", "2568.9~
$ INFO_ON_CO_LOCATORS <chr> NA, NA, NA, NA, NA, NA, NA, NA,~Saving to csv in local machine for future uses:
- Importing datas
5.1 importing Geospatial data
5.1.1. importing train station shp file
train_station = st_read(dsn = "data/geospatial",
layer = "MRTLRTStnPtt")
Reading layer `MRTLRTStnPtt' from data source
`C:\JunLonggggg\IS415\junlong-is415\_posts\2021-11-01-take-home-exercise-3\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 171 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6138.311 ymin: 27555.06 xmax: 45254.86 ymax: 47854.2
Projected CRS: SVY21st_crs(train_station)
Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Reading in the Planning Subzone Geospatial data.
mpsz = st_read(dsn = "data/geospatial",
layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source
`C:\JunLonggggg\IS415\junlong-is415\_posts\2021-11-01-take-home-exercise-3\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21st_crs(mpsz)
Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Setting the projected coordinate system to Singapore’s standard projection system of 3414.
train_station_3414 = st_set_crs(train_station, 3414)
mpsz_3414 = st_set_crs(mpsz, 3414)
To check if the change is successful:
st_crs(train_station_3414)
Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]tm_shape(mpsz_3414) +
tm_polygons() +
tm_shape(train_station_3414)+
tm_dots(alpha = 0.5,
size = 0.125)
Reading in the Aspatial data.
Resale Flats Data:
Adding lat lng:
resale = read_csv("data/aspatial/resale-flat-prices-based-on-registration-date-from-jan-2017-onwards.csv")
glimpse(resale)
- Data Wrangling
6.1 Formating geometric attributes
6.1.1 Splitting LatLng of supermarkets and Hawker Centres
6.1.2 Assigning spatial projection system of supermarkets and Hawker Centres to 3414
6.1.3 Associating geospatial property to resale flat data
resale["Latitude"] = NA
resale["Longitude"] = NA
sorted_resale_by_town = resale[order(resale$town),]
url = "https://developers.onemap.sg/commonapi/search"
for (row in 1:nrow(resale)){
print(row)
searchVal = paste(sorted_resale_by_town[row,'block'], sorted_resale_by_town[row,'street_name'])
query = list('searchVal' = searchVal, 'returnGeom' = "Y", 'getAddrDetails' ="N")
resp = GET(url, query = query, verbose())
sorted_resale_by_town$Latitude[row] = content(resp)$results[[1]]$LATITUDE
sorted_resale_by_town$Longitude[row] = content(resp)$results[[1]]$LONGITUDE
}
write.csv(sorted_resale_by_town,"data/aspatial/resale.csv",row.names = FALSE)
Read completed resale file:
resale = read_csv("data/aspatial/resale.csv")
glimpse(resale)
Rows: 15,901
Columns: 15
$ month <chr> "2019-01", "2019-01", "2019-01", "2019-~
$ town <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO~
$ flat_type <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROOM",~
$ address <chr> "204 ANG MO KIO AVE 3", "175 ANG MO KIO~
$ block <chr> "204", "175", "543", "118", "411", "546~
$ street_name <chr> "ANG MO KIO AVE 3", "ANG MO KIO AVE 4",~
$ storey_range <chr> "01 TO 03", "07 TO 09", "01 TO 03", "04~
$ floor_area_sqm <dbl> 92, 91, 92, 99, 92, 92, 92, 92, 93, 91,~
$ flat_model <chr> "New Generation", "New Generation", "Ne~
$ lease_commence_date <dbl> 1977, 1981, 1981, 1978, 1979, 1981, 197~
$ remaining_lease <chr> "57 years", "61 years 06 months", "61 y~
$ remaininglease_years <dbl> 57.00, 61.50, 61.08, 58.33, 59.58, 61.0~
$ resale_price <dbl> 330000, 360000, 370000, 375000, 380000,~
$ LATITUDE <dbl> 1.367368, 1.375723, 1.374301, 1.373296,~
$ LONGITUDE <dbl> 103.8439, 103.8371, 103.8562, 103.8355,~resale_3414 = st_as_sf(resale,
coords = c("LONGITUDE","LATITUDE"),
crs = 4326) %>%
st_transform(crs = 3414)
tm_shape(mpsz_3414) +
tm_polygons() +
tm_shape(resale_3414)+
tm_dots(alpha = 0.5,
size = 0.125)
resale_3414["prx_to_hawker"] = NA
resale_3414["prx_to_trainStn"] = NA
resale_3414["prx_to_supermarket"] = NA
resale_3414 <- resale_3414 %>%
mutate(`prx_to_hawker` = unlist(st_nn(resale_3414[1:nrow(resale_3414),], hawkerCentres_3414,k =1, returnDist = TRUE)[[2]])) %>%
mutate(`prx_to_trainStn` = unlist(st_nn(resale_3414[1:nrow(resale_3414),], train_station_3414,k =1, returnDist = TRUE)[[2]])) %>%
mutate(`prx_to_supermarket` = unlist(st_nn(resale_3414[1:nrow(resale_3414),], supermarkets_3414,k =1, returnDist = TRUE)[[2]]))
- EDA
ggplot(data=resale_3414, aes(x=`resale_price`)) +
geom_histogram(bins=20, color="black", fill="light blue")
resale_3414 <- resale_3414 %>%
mutate(`log_resale_price` = log(resale_price))
resale_3414 <- resale_3414 %>%
mutate(`max_floor` = as.numeric(str_sub(resale_3414$storey_range,-1)))
resale_3414$floor_area_sqm = as.numeric(resale_3414$floor_area_sqm)
AREA_SQM <- ggplot(data=resale_3414, aes(x= `floor_area_sqm`)) +
geom_histogram(bins=20, color="black", fill="light blue")
FLOOR_LVL <- ggplot(data=resale_3414, aes(x= `max_floor`)) +
geom_histogram(bins=20, color="black", fill="light blue")
REMAINING_LEASE <- ggplot(data=resale_3414, aes(x= `remaininglease_years`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_HAWKER = ggplot(data=resale_3414, aes(x=`prx_to_hawker`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_TRAINSTN = ggplot(data=resale_3414, aes(x=`prx_to_trainStn`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_SUPERMARKET = ggplot(data=resale_3414, aes(x=`prx_to_supermarket`)) +
geom_histogram(bins=20, color="black", fill="light blue")
ggarrange(AREA_SQM, FLOOR_LVL, REMAINING_LEASE, PROX_HAWKER, PROX_TRAINSTN, PROX_SUPERMARKET, ncol = 3, nrow = 4)
tm_shape(mpsz_3414)+
tm_polygons() +
tm_shape(resale_3414) +
tm_dots(col = "resale_price",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))
- Hedonic Price Modelling
8.1 Simple linear regression
resale_3414.slr <- lm(formula=resale_price ~ floor_area_sqm, data = resale_3414)
summary(resale_3414.slr)
Call:
lm(formula = resale_price ~ floor_area_sqm, data = resale_3414)
Residuals:
Min 1Q Median 3Q Max
-220690 -79631 -28690 36291 751169
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527814.2 12779.7 41.301 < 2e-16 ***
floor_area_sqm -990.3 133.9 -7.394 1.5e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 119900 on 15899 degrees of freedom
Multiple R-squared: 0.003426, Adjusted R-squared: 0.003364
F-statistic: 54.67 on 1 and 15899 DF, p-value: 1.5e-13The output can be formulated into:
y = 527814.2 - 990.3 x floor_area_sqm
The r-square value is 0.003426, which is signify that this formula is not a good gauge as the formula is only able to explain 0.3% of the data.
However, the hypothesis testing with p-value much lower than 0.0001 suggest that we can confidently reject the null hypothesis that mean is a good estimator of resale_price and that the simple linear regression model above is a poor estimator for resale_price
Both the coefficients have a p-value less than 0.0001 as well, thus we can confidently reject the null hypothesis that B0 and B1 are equal to 0, meaning that both B0 and B1 are good parameter estimates.
ggplot(data=resale_3414,
aes(x=`floor_area_sqm`, y=`resale_price`)) +
geom_point() +
geom_smooth(method = lm)
This shows that the relationship between floor_area_sqm and resale_price might not be able to approximate to a linear relationship.
8.2 Multiple Linear Regression
resale_tbl = as_tibble(resale_3414)
corrplot(cor(resale_tbl[, c("remaininglease_years","prx_to_hawker","prx_to_trainStn","prx_to_supermarket","max_floor","floor_area_sqm")]),
tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper")
From the plot above, we can see that none of the independent variable are highly correlated to each other, therefore, we can use the variables.
resale_tbl.mlr <- lm(formula = resale_price ~ remaininglease_years + floor_area_sqm + max_floor + prx_to_hawker + prx_to_trainStn + prx_to_supermarket, data=resale_3414)
summary(resale_tbl.mlr)
Call:
lm(formula = resale_price ~ remaininglease_years + floor_area_sqm +
max_floor + prx_to_hawker + prx_to_trainStn + prx_to_supermarket,
data = resale_3414)
Residuals:
Min 1Q Median 3Q Max
-197602 -72132 -21827 40103 674490
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 142113.774 13753.774 10.333 <2e-16 ***
remaininglease_years 3262.168 67.431 48.378 <2e-16 ***
floor_area_sqm 1371.386 121.423 11.294 <2e-16 ***
max_floor 60.417 315.951 0.191 0.848
prx_to_hawker -68.923 1.649 -41.790 <2e-16 ***
prx_to_trainStn -47.715 2.200 -21.693 <2e-16 ***
prx_to_supermarket -45.759 5.454 -8.390 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 104400 on 15894 degrees of freedom
Multiple R-squared: 0.2455, Adjusted R-squared: 0.2452
F-statistic: 861.8 on 6 and 15894 DF, p-value: < 2.2e-16From the statistical summary, we can see that not all variables are statistically significant, thus we will need to revise the model by removing these statistically insignificant variables. Namely: * max_floor
resale_tbl.mlr1 <- lm(formula = resale_price ~ remaininglease_years + floor_area_sqm + prx_to_hawker + prx_to_trainStn + prx_to_supermarket, data=resale_3414)
ols_regress(resale_tbl.mlr1)
Model Summary
-----------------------------------------------------------------------
R 0.495 RMSE 104356.809
R-Squared 0.245 Coef. Var 24.068
Adj. R-Squared 0.245 MSE 10890343642.219
Pred R-Squared 0.245 MAE 77678.476
-----------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
ANOVA
---------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
---------------------------------------------------------------------------------
Regression 5.631684e+13 5 1.126337e+13 1034.253 0.0000
Residual 1.73102e+14 15895 10890343642.219
Total 2.294188e+14 15900
---------------------------------------------------------------------------------
Parameter Estimates
--------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
--------------------------------------------------------------------------------------------------------------
(Intercept) 142448.724 13641.365 10.442 0.000 115710.103 169187.345
remaininglease_years 3262.077 67.428 0.349 48.379 0.000 3129.912 3394.243
floor_area_sqm 1371.204 121.416 0.081 11.293 0.000 1133.215 1609.193
prx_to_hawker -68.919 1.649 -0.296 -41.793 0.000 -72.151 -65.687
prx_to_trainStn -47.719 2.199 -0.153 -21.697 0.000 -52.030 -43.408
prx_to_supermarket -45.747 5.453 -0.060 -8.389 0.000 -56.437 -35.058
--------------------------------------------------------------------------------------------------------------Assumptions of linear regression models
Linearity Assumption: Relationship between dependent and independent variables is (approximately) linear.
Normality Assumption: The residual errors are assumed to be normally distributed.
Homogenuity of residual variance: The residuals are assumed to have a constant variance (homoscedasticity).
Residuals are independent to each other
(Optional) Errors are normally distributed with a population mean of 0.
Checking for multicollinearity
We will explore the use of olsrr, a package specially programmed for performing Ordinary Least Squared (OLS) regression.
Some of the useful methods includes: * comprehensive regression output * residual diagnostics * measures of influence * heteroskedasticity tests * collinearity diagnostics * model fit assessment * variable contribution assessment * variable selection procedures
We will be using ols_vid_tol() method from olsrr package for multicollinearity.
ols_vif_tol(resale_tbl.mlr1)
Variables Tolerance VIF
1 remaininglease_years 0.9130828 1.095191
2 floor_area_sqm 0.9215493 1.085129
3 prx_to_hawker 0.9462454 1.056808
4 prx_to_trainStn 0.9508515 1.051689
5 prx_to_supermarket 0.9301457 1.075100A good judgement of multicollinearity would be if the VIF is above 10. Since none of the variables exceed the VIF value of 10, we can safely conclude that there are no sign of multicollinearity among the independent variables.
Testing for non-linearity
In multiple linear regression, we need to test for linearity and additivity of the relationship between dependent and independent variables. We can do so using ols_plot_resid_fit() from olsrr package to perform linearity assumption test.
ols_plot_resid_fit(resale_tbl.mlr1)
From the figure above, we can see that the residual roughly revolves around the 0 line, thus we can safely conclude that the relationships between the dependent and the independent variables are linear.
Testing for normality assumption
Next, we still need to test if the residual errors are normally distributed using ols_plot_resid_hist() to perform normality assumption test.
ols_plot_resid_hist(resale_tbl.mlr1)
The figure above shows that the residual of the multiple linear regression model resemble a rather flat normal distribution.
Testing for Spatial Autocorrelation
The hedonic model we are building are using geographically referenced attribute, thus we should visualize the residual of the hedonic pricing model.
To perform spatial autocorrelation test, we will have to convert condo_resale.sf into SpatialPointDataFrame.
mlr.output <- as.data.frame(resale_tbl.mlr1$residuals)
Joining the newly created data frame with condo_resale.sf
resale_tbl.res.sf <- cbind(resale_3414,
resale_tbl.mlr1$residuals) %>%
rename(`MLR_RES` = `resale_tbl.mlr1.residuals`)
Converting the sf object into SpatialPointDataFrame using spdep package:
resale_tbl.sp <- as_Spatial(resale_tbl.res.sf)
resale_tbl.sp
class : SpatialPointsDataFrame
features : 15901
extent : 11597.31, 42623.63, 28217.39, 48741.06 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 19
names : month, town, flat_type, address, block, street_name, storey_range, floor_area_sqm, flat_model, lease_commence_date, remaining_lease, remaininglease_years, resale_price, prx_to_hawker, prx_to_trainStn, ...
min values : 2019-01, ANG MO KIO, 4 ROOM, 1 CHAI CHEE RD, 1, ADMIRALTY DR, 01 TO 03, 74, Adjoined flat, 1967, 45 years 06 months, 45.5, 218000, 33.3358643817954, 22.0407324774434, ...
max values : 2020-09, YISHUN, 4 ROOM, 9B BOON TIONG RD, 9B, YUNG SHENG RD, 49 TO 51, 138, Type S1, 2018, 97 years, 97, 1186888, 2867.63031236184, 2130.60636038504, ... Now we can plot a interactive visualization of the residual on a map itself.
First, setting the tmap mode to “view”, or interactive.
tmap_mode("view")
Plotting the geographically referenced residual:
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz_3414)+
tm_polygons(alpha = 0.4) +
tm_shape(resale_tbl.res.sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))
Setting back the tmap mode to “plot”:
tmap_mode("plot")
The above plot does show signs of spatial autocorrelation since there are some parts with concentrated high MLR_RES values, however, to be more definitive, we will use Moran’s I test to confirm our observation.
First, computing the distance-based weight matrix using dnearneigh() function of spdep:
nb <- dnearneigh(coordinates(resale_tbl.sp), 0, 1500, longlat = FALSE)
summary(nb)
Neighbour list object:
Number of regions: 15901
Number of nonzero links: 10219360
Percentage nonzero weights: 4.0418
Average number of links: 642.6866
Link number distribution:
2 7 14 25 26 31 32 46 56 57 60 65 68 69
3 1 14 15 5 4 2 47 4 4 5 2 4 1
71 72 75 79 86 88 89 90 97 99 101 103 106 109
12 1 1 78 3 5 4 3 8 8 6 2 2 5
110 112 115 117 118 119 120 121 122 123 124 125 126 128
8 3 6 1 9 6 5 7 4 22 7 55 21 30
130 131 132 133 134 135 136 137 138 139 140 141 142 143
1 14 6 14 7 5 5 9 2 28 4 2 8 15
145 146 147 148 149 150 151 152 153 154 155 156 157 158
9 6 17 6 1 1 21 20 13 7 3 8 9 5
159 160 161 162 163 164 165 166 167 168 169 170 171 173
17 6 3 2 12 6 6 3 11 3 11 3 8 14
174 175 176 177 178 179 180 181 182 183 184 185 186 187
2 28 14 23 10 17 11 7 5 12 12 9 37 22
188 189 190 191 192 193 194 195 196 197 198 199 200 201
14 3 5 6 10 7 2 8 4 7 21 8 14 18
202 203 204 205 206 207 208 209 210 211 212 213 214 215
28 3 15 14 3 5 22 4 1 5 8 4 14 21
216 217 218 219 220 221 222 223 224 225 226 227 228 229
6 3 2 12 24 28 38 3 10 10 4 20 25 3
230 231 232 233 234 235 236 237 238 239 240 241 242 243
10 15 3 14 13 37 10 2 21 10 31 24 8 8
244 245 246 247 248 249 250 251 252 253 254 255 256 257
11 11 3 14 13 20 6 24 8 23 18 15 15 13
258 259 260 261 262 263 264 265 266 267 268 269 270 271
7 4 7 11 14 5 26 13 3 27 34 15 1 19
272 273 274 275 276 277 278 279 280 281 282 283 284 285
34 55 19 19 24 17 58 12 54 29 31 24 33 27
286 287 288 289 290 291 292 293 294 295 296 297 298 299
11 62 51 29 21 33 71 39 14 43 8 20 30 25
300 301 302 303 304 305 306 307 308 309 310 311 312 313
21 23 34 21 31 32 22 12 19 4 13 11 11 24
314 315 316 317 318 319 320 321 322 323 324 325 326 327
7 26 18 14 43 23 19 24 26 24 39 21 19 42
328 329 330 331 332 333 334 335 336 337 338 339 340 341
24 23 23 31 12 19 27 34 3 27 35 25 21 42
342 343 344 345 346 347 348 349 350 351 352 353 354 355
6 28 19 18 12 28 10 41 20 23 32 10 34 30
356 357 358 359 360 361 362 363 364 365 366 367 368 369
20 6 20 18 43 24 7 12 43 12 42 32 10 36
370 371 372 373 374 375 376 377 378 379 380 381 382 383
4 31 18 17 45 19 37 35 10 24 14 13 23 17
384 385 386 387 388 389 390 391 392 393 394 395 396 397
4 35 32 31 22 16 40 15 16 16 20 22 23 31
398 399 400 401 402 403 404 405 406 407 408 409 410 411
19 12 27 21 24 18 32 8 16 16 23 3 23 18
412 413 414 415 416 417 418 419 420 421 422 423 424 425
26 22 9 26 16 14 13 66 20 12 13 82 14 19
426 427 428 429 430 431 432 433 434 435 436 437 438 439
25 23 30 26 9 29 18 29 32 20 35 12 25 21
440 441 442 443 444 445 446 447 448 449 450 451 452 453
14 27 11 10 1 28 10 13 27 24 15 11 35 26
454 455 456 457 458 459 460 461 462 463 464 465 466 467
11 24 21 17 58 33 3 15 17 6 31 15 7 20
468 469 470 471 472 473 474 475 476 477 478 479 480 481
28 6 19 21 9 19 23 8 24 18 33 30 25 20
482 483 484 485 486 487 488 489 490 491 492 493 494 495
9 9 8 23 15 16 15 10 34 8 4 18 11 20
496 497 498 499 500 501 502 503 504 505 506 507 508 509
5 19 6 8 10 5 4 26 17 22 10 48 18 6
510 511 512 513 514 515 516 517 518 519 520 521 522 523
24 34 21 34 1 13 14 4 7 7 7 4 9 18
524 525 526 527 528 529 530 531 532 533 534 535 536 537
11 10 8 10 7 50 21 14 20 12 10 17 21 7
538 539 540 541 542 543 544 545 546 547 548 549 550 551
3 9 4 6 3 16 24 15 11 5 8 13 8 18
552 553 554 555 556 557 558 559 560 561 562 563 564 565
8 9 5 12 3 11 18 22 14 7 5 21 10 15
566 567 568 569 570 571 572 573 574 575 576 577 578 579
33 17 22 15 12 17 7 8 21 14 42 4 27 11
580 582 583 584 585 586 587 588 589 590 591 592 593 594
13 12 10 16 7 21 12 5 12 31 18 23 8 13
595 596 597 598 599 600 601 602 603 604 605 606 607 608
13 13 24 12 8 17 10 6 12 18 10 8 18 11
609 610 611 612 613 614 615 616 617 618 619 620 621 622
12 14 29 22 2 9 10 7 27 26 12 4 10 1
623 624 625 626 627 628 629 630 631 632 633 634 635 636
2 26 7 14 21 16 5 5 7 4 3 22 4 13
637 638 639 640 641 642 643 644 645 646 647 648 649 650
19 24 5 8 5 17 9 7 14 3 33 10 5 14
651 652 653 654 655 656 657 658 659 660 661 662 664 666
5 39 9 5 10 10 5 4 2 11 21 4 18 3
667 668 669 670 671 672 673 674 675 676 677 678 679 680
2 4 17 14 15 5 9 3 9 22 6 12 13 14
681 682 683 684 686 687 688 689 690 691 692 693 694 695
8 7 5 30 27 4 34 1 19 20 5 8 22 9
696 697 698 699 701 702 703 704 705 706 707 708 709 710
6 16 17 14 6 10 7 10 14 26 6 14 2 7
711 712 713 714 715 716 717 718 719 720 721 722 723 724
6 9 4 2 31 11 9 13 7 33 33 5 14 11
725 726 728 729 730 731 732 733 734 735 736 737 738 739
2 4 7 2 5 2 26 2 10 1 12 1 5 2
740 741 742 743 744 745 746 747 748 749 750 751 752 753
1 13 8 11 16 2 8 23 13 16 18 8 6 26
754 755 756 757 758 759 760 761 762 763 764 765 766 767
6 24 11 12 4 15 5 27 11 3 1 11 7 6
768 769 770 771 772 773 774 775 776 777 778 779 780 781
4 18 27 31 3 23 21 6 5 17 12 19 19 17
782 783 784 785 786 787 788 789 790 791 792 793 794 795
26 9 10 34 16 16 13 7 4 14 15 21 13 9
796 797 798 799 800 801 802 803 804 805 806 807 808 809
3 17 19 9 4 9 46 14 11 1 6 12 31 9
810 811 812 813 814 815 816 817 818 819 820 821 822 823
21 10 19 36 2 48 4 11 16 6 5 3 46 20
824 825 826 827 828 829 830 831 832 833 834 835 836 837
31 8 18 8 39 11 6 4 1 14 10 9 24 30
838 839 840 841 842 843 844 845 846 847 848 849 850 851
14 6 30 11 17 7 9 12 8 12 10 16 13 13
852 853 854 855 856 857 858 859 860 861 862 863 864 865
19 21 33 16 12 4 4 12 16 3 9 20 16 6
866 867 868 869 870 871 872 873 874 875 876 877 878 879
11 11 31 5 18 13 15 3 2 5 4 2 19 7
880 881 882 883 884 885 886 887 888 889 890 891 892 893
11 5 5 12 11 5 3 10 10 4 3 28 21 17
894 895 896 897 898 899 900 901 902 903 904 905 906 907
3 3 9 1 6 10 11 24 5 13 12 5 38 11
908 909 910 911 912 913 914 915 917 918 919 920 921 922
4 6 3 4 11 14 2 8 4 6 4 19 4 12
923 924 925 926 927 928 929 930 931 932 933 934 935 936
30 23 8 5 3 5 2 18 2 11 6 17 4 1
938 939 940 941 942 943 944 945 946 950 951 952 953 954
13 16 15 3 3 22 8 3 3 4 4 6 4 21
955 956 958 961 962 964 965 966 967 968 969 970 971 974
5 9 1 2 7 2 5 7 10 1 8 29 10 5
975 976 978 979 980 981 982 983 984 985 986 987 988 989
10 3 9 3 22 1 1 11 31 5 11 5 4 1
990 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1005
2 24 6 1 5 1 2 5 4 6 1 8 5 20
1008 1009 1010 1011 1012 1013 1014 1015 1018 1019 1020 1021 1022 1023
5 8 20 5 8 5 5 1 13 3 12 24 17 2
1024 1025 1026 1027 1029 1030 1032 1033 1034 1035 1036 1037 1039 1041
8 16 9 11 7 4 13 4 2 3 29 6 14 6
1043 1045 1046 1047 1048 1049 1050 1051 1053 1054 1055 1057 1059 1060
13 7 6 2 7 9 3 11 5 6 25 2 1 31
1061 1062 1065 1066 1067 1068 1069 1070 1073 1074 1075 1080 1081 1084
14 1 3 7 5 1 8 9 3 6 2 1 9 5
1086 1087 1088 1089 1092 1093 1094 1095 1096 1097 1098 1100 1103 1104
15 1 6 3 2 6 12 3 7 17 8 10 8 8
1108 1111 1113 1114 1117 1118 1120 1122 1123 1124 1125 1127 1131 1133
3 5 2 4 21 20 5 6 9 6 4 12 8 1
1135 1137 1138 1139 1140 1141 1143 1144 1145 1146 1147 1148 1149 1151
33 2 7 9 6 5 15 12 15 5 12 2 15 8
1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165 1166 1167
11 2 7 21 6 8 1 9 7 14 10 3 9 2
1168 1170 1171 1172 1173 1174 1175 1176 1177 1179 1180 1181 1182 1183
10 15 4 41 14 5 13 10 12 14 13 12 2 3
1185 1186 1187 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199
7 2 1 11 6 14 2 9 10 8 1 2 12 2
1200 1201 1203 1204 1205 1206 1207 1208 1210 1213 1214 1216 1217 1218
20 1 10 18 6 5 4 13 4 5 8 16 3 11
1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1234 1235
2 19 45 5 41 2 7 14 14 9 6 15 11 4
1236 1237 1238 1239 1240 1241 1242 1244 1245 1246 1247 1248 1250 1254
7 31 13 14 7 1 5 4 8 14 11 3 1 1
1255 1256 1258 1259 1263 1264 1266 1267 1268 1269 1270 1271 1272 1273
3 12 3 1 6 6 1 7 3 6 7 6 5 14
1274 1275 1279 1281 1282 1283 1284 1286 1287 1288 1289 1291 1292 1294
2 12 10 10 3 16 2 14 1 1 3 10 9 4
1295 1296 1297 1302 1304 1305 1307 1308 1309 1310 1311 1312 1313 1314
4 5 4 14 3 4 3 7 8 18 1 8 6 30
1315 1316 1317 1319 1322 1324 1325 1327 1328 1330 1331 1333 1334 1335
1 1 14 7 17 3 5 4 2 10 2 17 3 1
1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350
10 5 14 8 7 27 1 1 9 12 13 18 3 18
1351 1352 1353 1357 1358 1362 1363 1365 1368 1369 1370 1372 1373 1374
6 11 13 8 8 21 8 8 17 11 2 6 1 12
1376 1377 1378 1379 1381 1382 1383 1384 1385 1386 1387 1390 1391 1392
10 3 12 5 6 5 24 10 6 4 10 8 12 5
1394 1396 1397 1399 1400 1401 1403 1406 1407 1408 1410 1413 1414 1416
6 6 21 8 2 6 7 15 6 2 14 4 1 20
1417 1421 1422 1423 1425 1426 1429 1431 1432 1434 1435 1437 1440 1442
4 18 1 1 2 3 1 2 2 1 1 1 11 2
1445 1447 1452 1454 1458 1460 1461 1465 1466 1467 1468 1472 1473 1474
19 2 10 2 8 11 1 2 3 1 4 1 1 2
1475 1476 1477 1479 1480 1481 1486 1488 1492 1493 1494 1495 1496 1497
5 1 2 1 2 2 1 19 4 3 1 4 4 1
1498 1499 1500 1502 1507 1519 1526 1527 1528 1531 1534 1536 1540 1543
12 1 1 8 1 2 3 2 3 6 6 6 4 4
1548 1549 1551 1552 1553 1561 1564 1565 1567 1569 1573 1577 1580 1583
2 3 2 1 7 4 2 3 3 12 2 1 2 4
1587 1588 1593 1597 1598 1603 1604 1608 1617 1618 1624 1626 1637 1638
1 8 4 3 6 1 1 9 3 1 1 3 2 16
1647 1654 1655 1676 1685 1695 1701 1705 1728 1734 1738 1743 1745 1752
1 3 4 1 1 1 1 5 1 1 3 1 4 3
1758 1765 1771 1774 1775 1800 1808 1811 1817 1852 1875 1882 1922 1951
2 3 4 4 1 4 5 4 1 3 3 1 2 5
1965
4
3 least connected regions:
3093 4752 5564 with 2 links
4 most connected regions:
3260 8169 12559 13540 with 1965 linksNext, nb2listw() of spdep packge will be used to convert the output neighbours lists (i.e. nb) into a spatial weights.
nb_lw <- nb2listw(nb, style = 'W')
summary(nb_lw)
Characteristics of weights list object:
Neighbour list object:
Number of regions: 15901
Number of nonzero links: 10219360
Percentage nonzero weights: 4.0418
Average number of links: 642.6866
Link number distribution:
2 7 14 25 26 31 32 46 56 57 60 65 68 69
3 1 14 15 5 4 2 47 4 4 5 2 4 1
71 72 75 79 86 88 89 90 97 99 101 103 106 109
12 1 1 78 3 5 4 3 8 8 6 2 2 5
110 112 115 117 118 119 120 121 122 123 124 125 126 128
8 3 6 1 9 6 5 7 4 22 7 55 21 30
130 131 132 133 134 135 136 137 138 139 140 141 142 143
1 14 6 14 7 5 5 9 2 28 4 2 8 15
145 146 147 148 149 150 151 152 153 154 155 156 157 158
9 6 17 6 1 1 21 20 13 7 3 8 9 5
159 160 161 162 163 164 165 166 167 168 169 170 171 173
17 6 3 2 12 6 6 3 11 3 11 3 8 14
174 175 176 177 178 179 180 181 182 183 184 185 186 187
2 28 14 23 10 17 11 7 5 12 12 9 37 22
188 189 190 191 192 193 194 195 196 197 198 199 200 201
14 3 5 6 10 7 2 8 4 7 21 8 14 18
202 203 204 205 206 207 208 209 210 211 212 213 214 215
28 3 15 14 3 5 22 4 1 5 8 4 14 21
216 217 218 219 220 221 222 223 224 225 226 227 228 229
6 3 2 12 24 28 38 3 10 10 4 20 25 3
230 231 232 233 234 235 236 237 238 239 240 241 242 243
10 15 3 14 13 37 10 2 21 10 31 24 8 8
244 245 246 247 248 249 250 251 252 253 254 255 256 257
11 11 3 14 13 20 6 24 8 23 18 15 15 13
258 259 260 261 262 263 264 265 266 267 268 269 270 271
7 4 7 11 14 5 26 13 3 27 34 15 1 19
272 273 274 275 276 277 278 279 280 281 282 283 284 285
34 55 19 19 24 17 58 12 54 29 31 24 33 27
286 287 288 289 290 291 292 293 294 295 296 297 298 299
11 62 51 29 21 33 71 39 14 43 8 20 30 25
300 301 302 303 304 305 306 307 308 309 310 311 312 313
21 23 34 21 31 32 22 12 19 4 13 11 11 24
314 315 316 317 318 319 320 321 322 323 324 325 326 327
7 26 18 14 43 23 19 24 26 24 39 21 19 42
328 329 330 331 332 333 334 335 336 337 338 339 340 341
24 23 23 31 12 19 27 34 3 27 35 25 21 42
342 343 344 345 346 347 348 349 350 351 352 353 354 355
6 28 19 18 12 28 10 41 20 23 32 10 34 30
356 357 358 359 360 361 362 363 364 365 366 367 368 369
20 6 20 18 43 24 7 12 43 12 42 32 10 36
370 371 372 373 374 375 376 377 378 379 380 381 382 383
4 31 18 17 45 19 37 35 10 24 14 13 23 17
384 385 386 387 388 389 390 391 392 393 394 395 396 397
4 35 32 31 22 16 40 15 16 16 20 22 23 31
398 399 400 401 402 403 404 405 406 407 408 409 410 411
19 12 27 21 24 18 32 8 16 16 23 3 23 18
412 413 414 415 416 417 418 419 420 421 422 423 424 425
26 22 9 26 16 14 13 66 20 12 13 82 14 19
426 427 428 429 430 431 432 433 434 435 436 437 438 439
25 23 30 26 9 29 18 29 32 20 35 12 25 21
440 441 442 443 444 445 446 447 448 449 450 451 452 453
14 27 11 10 1 28 10 13 27 24 15 11 35 26
454 455 456 457 458 459 460 461 462 463 464 465 466 467
11 24 21 17 58 33 3 15 17 6 31 15 7 20
468 469 470 471 472 473 474 475 476 477 478 479 480 481
28 6 19 21 9 19 23 8 24 18 33 30 25 20
482 483 484 485 486 487 488 489 490 491 492 493 494 495
9 9 8 23 15 16 15 10 34 8 4 18 11 20
496 497 498 499 500 501 502 503 504 505 506 507 508 509
5 19 6 8 10 5 4 26 17 22 10 48 18 6
510 511 512 513 514 515 516 517 518 519 520 521 522 523
24 34 21 34 1 13 14 4 7 7 7 4 9 18
524 525 526 527 528 529 530 531 532 533 534 535 536 537
11 10 8 10 7 50 21 14 20 12 10 17 21 7
538 539 540 541 542 543 544 545 546 547 548 549 550 551
3 9 4 6 3 16 24 15 11 5 8 13 8 18
552 553 554 555 556 557 558 559 560 561 562 563 564 565
8 9 5 12 3 11 18 22 14 7 5 21 10 15
566 567 568 569 570 571 572 573 574 575 576 577 578 579
33 17 22 15 12 17 7 8 21 14 42 4 27 11
580 582 583 584 585 586 587 588 589 590 591 592 593 594
13 12 10 16 7 21 12 5 12 31 18 23 8 13
595 596 597 598 599 600 601 602 603 604 605 606 607 608
13 13 24 12 8 17 10 6 12 18 10 8 18 11
609 610 611 612 613 614 615 616 617 618 619 620 621 622
12 14 29 22 2 9 10 7 27 26 12 4 10 1
623 624 625 626 627 628 629 630 631 632 633 634 635 636
2 26 7 14 21 16 5 5 7 4 3 22 4 13
637 638 639 640 641 642 643 644 645 646 647 648 649 650
19 24 5 8 5 17 9 7 14 3 33 10 5 14
651 652 653 654 655 656 657 658 659 660 661 662 664 666
5 39 9 5 10 10 5 4 2 11 21 4 18 3
667 668 669 670 671 672 673 674 675 676 677 678 679 680
2 4 17 14 15 5 9 3 9 22 6 12 13 14
681 682 683 684 686 687 688 689 690 691 692 693 694 695
8 7 5 30 27 4 34 1 19 20 5 8 22 9
696 697 698 699 701 702 703 704 705 706 707 708 709 710
6 16 17 14 6 10 7 10 14 26 6 14 2 7
711 712 713 714 715 716 717 718 719 720 721 722 723 724
6 9 4 2 31 11 9 13 7 33 33 5 14 11
725 726 728 729 730 731 732 733 734 735 736 737 738 739
2 4 7 2 5 2 26 2 10 1 12 1 5 2
740 741 742 743 744 745 746 747 748 749 750 751 752 753
1 13 8 11 16 2 8 23 13 16 18 8 6 26
754 755 756 757 758 759 760 761 762 763 764 765 766 767
6 24 11 12 4 15 5 27 11 3 1 11 7 6
768 769 770 771 772 773 774 775 776 777 778 779 780 781
4 18 27 31 3 23 21 6 5 17 12 19 19 17
782 783 784 785 786 787 788 789 790 791 792 793 794 795
26 9 10 34 16 16 13 7 4 14 15 21 13 9
796 797 798 799 800 801 802 803 804 805 806 807 808 809
3 17 19 9 4 9 46 14 11 1 6 12 31 9
810 811 812 813 814 815 816 817 818 819 820 821 822 823
21 10 19 36 2 48 4 11 16 6 5 3 46 20
824 825 826 827 828 829 830 831 832 833 834 835 836 837
31 8 18 8 39 11 6 4 1 14 10 9 24 30
838 839 840 841 842 843 844 845 846 847 848 849 850 851
14 6 30 11 17 7 9 12 8 12 10 16 13 13
852 853 854 855 856 857 858 859 860 861 862 863 864 865
19 21 33 16 12 4 4 12 16 3 9 20 16 6
866 867 868 869 870 871 872 873 874 875 876 877 878 879
11 11 31 5 18 13 15 3 2 5 4 2 19 7
880 881 882 883 884 885 886 887 888 889 890 891 892 893
11 5 5 12 11 5 3 10 10 4 3 28 21 17
894 895 896 897 898 899 900 901 902 903 904 905 906 907
3 3 9 1 6 10 11 24 5 13 12 5 38 11
908 909 910 911 912 913 914 915 917 918 919 920 921 922
4 6 3 4 11 14 2 8 4 6 4 19 4 12
923 924 925 926 927 928 929 930 931 932 933 934 935 936
30 23 8 5 3 5 2 18 2 11 6 17 4 1
938 939 940 941 942 943 944 945 946 950 951 952 953 954
13 16 15 3 3 22 8 3 3 4 4 6 4 21
955 956 958 961 962 964 965 966 967 968 969 970 971 974
5 9 1 2 7 2 5 7 10 1 8 29 10 5
975 976 978 979 980 981 982 983 984 985 986 987 988 989
10 3 9 3 22 1 1 11 31 5 11 5 4 1
990 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1005
2 24 6 1 5 1 2 5 4 6 1 8 5 20
1008 1009 1010 1011 1012 1013 1014 1015 1018 1019 1020 1021 1022 1023
5 8 20 5 8 5 5 1 13 3 12 24 17 2
1024 1025 1026 1027 1029 1030 1032 1033 1034 1035 1036 1037 1039 1041
8 16 9 11 7 4 13 4 2 3 29 6 14 6
1043 1045 1046 1047 1048 1049 1050 1051 1053 1054 1055 1057 1059 1060
13 7 6 2 7 9 3 11 5 6 25 2 1 31
1061 1062 1065 1066 1067 1068 1069 1070 1073 1074 1075 1080 1081 1084
14 1 3 7 5 1 8 9 3 6 2 1 9 5
1086 1087 1088 1089 1092 1093 1094 1095 1096 1097 1098 1100 1103 1104
15 1 6 3 2 6 12 3 7 17 8 10 8 8
1108 1111 1113 1114 1117 1118 1120 1122 1123 1124 1125 1127 1131 1133
3 5 2 4 21 20 5 6 9 6 4 12 8 1
1135 1137 1138 1139 1140 1141 1143 1144 1145 1146 1147 1148 1149 1151
33 2 7 9 6 5 15 12 15 5 12 2 15 8
1152 1153 1154 1156 1157 1158 1160 1161 1162 1163 1164 1165 1166 1167
11 2 7 21 6 8 1 9 7 14 10 3 9 2
1168 1170 1171 1172 1173 1174 1175 1176 1177 1179 1180 1181 1182 1183
10 15 4 41 14 5 13 10 12 14 13 12 2 3
1185 1186 1187 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199
7 2 1 11 6 14 2 9 10 8 1 2 12 2
1200 1201 1203 1204 1205 1206 1207 1208 1210 1213 1214 1216 1217 1218
20 1 10 18 6 5 4 13 4 5 8 16 3 11
1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1234 1235
2 19 45 5 41 2 7 14 14 9 6 15 11 4
1236 1237 1238 1239 1240 1241 1242 1244 1245 1246 1247 1248 1250 1254
7 31 13 14 7 1 5 4 8 14 11 3 1 1
1255 1256 1258 1259 1263 1264 1266 1267 1268 1269 1270 1271 1272 1273
3 12 3 1 6 6 1 7 3 6 7 6 5 14
1274 1275 1279 1281 1282 1283 1284 1286 1287 1288 1289 1291 1292 1294
2 12 10 10 3 16 2 14 1 1 3 10 9 4
1295 1296 1297 1302 1304 1305 1307 1308 1309 1310 1311 1312 1313 1314
4 5 4 14 3 4 3 7 8 18 1 8 6 30
1315 1316 1317 1319 1322 1324 1325 1327 1328 1330 1331 1333 1334 1335
1 1 14 7 17 3 5 4 2 10 2 17 3 1
1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350
10 5 14 8 7 27 1 1 9 12 13 18 3 18
1351 1352 1353 1357 1358 1362 1363 1365 1368 1369 1370 1372 1373 1374
6 11 13 8 8 21 8 8 17 11 2 6 1 12
1376 1377 1378 1379 1381 1382 1383 1384 1385 1386 1387 1390 1391 1392
10 3 12 5 6 5 24 10 6 4 10 8 12 5
1394 1396 1397 1399 1400 1401 1403 1406 1407 1408 1410 1413 1414 1416
6 6 21 8 2 6 7 15 6 2 14 4 1 20
1417 1421 1422 1423 1425 1426 1429 1431 1432 1434 1435 1437 1440 1442
4 18 1 1 2 3 1 2 2 1 1 1 11 2
1445 1447 1452 1454 1458 1460 1461 1465 1466 1467 1468 1472 1473 1474
19 2 10 2 8 11 1 2 3 1 4 1 1 2
1475 1476 1477 1479 1480 1481 1486 1488 1492 1493 1494 1495 1496 1497
5 1 2 1 2 2 1 19 4 3 1 4 4 1
1498 1499 1500 1502 1507 1519 1526 1527 1528 1531 1534 1536 1540 1543
12 1 1 8 1 2 3 2 3 6 6 6 4 4
1548 1549 1551 1552 1553 1561 1564 1565 1567 1569 1573 1577 1580 1583
2 3 2 1 7 4 2 3 3 12 2 1 2 4
1587 1588 1593 1597 1598 1603 1604 1608 1617 1618 1624 1626 1637 1638
1 8 4 3 6 1 1 9 3 1 1 3 2 16
1647 1654 1655 1676 1685 1695 1701 1705 1728 1734 1738 1743 1745 1752
1 3 4 1 1 1 1 5 1 1 3 1 4 3
1758 1765 1771 1774 1775 1800 1808 1811 1817 1852 1875 1882 1922 1951
2 3 4 4 1 4 5 4 1 3 3 1 2 5
1965
4
3 least connected regions:
3093 4752 5564 with 2 links
4 most connected regions:
3260 8169 12559 13540 with 1965 links
Weights style: W
Weights constants summary:
n nn S0 S1 S2
W 15901 252841801 15901 79.6504 64104.78Next, lm.morantest() of spdep package will be used to perform Moran’s I test for residual spatial autocorrelation
lm.morantest(resale_tbl.mlr1, nb_lw)
Global Moran I for regression residuals
data:
model: lm(formula = resale_price ~ remaininglease_years +
floor_area_sqm + prx_to_hawker + prx_to_trainStn +
prx_to_supermarket, data = resale_3414)
weights: nb_lw
Moran I statistic standard deviate = 1249.4, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
6.709842e-01 -1.777304e-04 2.885511e-07 Based on the global moran’s I test, the residual spatial autocorrelation shows that it’s p-value is less than 2.2 x 10^-16, which is a significantly small value, and is much lower than the alpha value of 0.05, hence we will reject the null hypothesis that the residuals are randomly distribute, in other words, the residuals resembles cluster distributions.
Building Hedonic Pricing Models using GWmodel
In this section, we will learn how to model hedonic pricing using both the fixed and adaptive bandwidth schemes
Building Adaptive Bandwidth GWR Model
In this section, we will calibrate the gwr-absed hedonic pricing model by using adaptive bandwidth approach.
Computing the adaptive bandwidth
We will be using bw.ger() to determine the recommended data point to use.
The code chunk used look very similar to the one used to compute the fixed bandwidth except the adaptive argument has changed to TRUE.
bw.adaptive <- bw.gwr(formula = resale_price ~ remaininglease_years + floor_area_sqm + prx_to_hawker + prx_to_trainStn + prx_to_supermarket, data=resale_tbl.sp, approach="CV", kernel="gaussian",
adaptive=TRUE, longlat=FALSE)
Take a cup of tea and have a break, it will take a few minutes.
-----A kind suggestion from GWmodel development group
Adaptive bandwidth: 9834 CV score: 1.477862e+14
Adaptive bandwidth: 6086 CV score: 1.343193e+14
Adaptive bandwidth: 3767 CV score: 1.168869e+14
Adaptive bandwidth: 2337 CV score: 9.445512e+13
Adaptive bandwidth: 1449 CV score: 6.53688e+13
Adaptive bandwidth: 905 CV score: 4.59035e+13
Adaptive bandwidth: 563 CV score: 3.621509e+13
Adaptive bandwidth: 358 CV score: 3.051304e+13
Adaptive bandwidth: 224 CV score: 2.639004e+13
Adaptive bandwidth: 149 CV score: 2.362456e+13
Adaptive bandwidth: 94 CV score: 2.043158e+13
Adaptive bandwidth: 69 CV score: 1.824158e+13
Adaptive bandwidth: 44 CV score: 1.670637e+13
Adaptive bandwidth: 38 CV score: 1.635281e+13
Adaptive bandwidth: 25 CV score: NaN
Adaptive bandwidth: 37 CV score: 1.630511e+13
Adaptive bandwidth: 45 CV score: 1.674146e+13
Adaptive bandwidth: 40 CV score: 1.651203e+13
Adaptive bandwidth: 43 CV score: 1.664289e+13
Adaptive bandwidth: 41 CV score: 1.654087e+13
Adaptive bandwidth: 42 CV score: 1.660254e+13
Adaptive bandwidth: 41 CV score: 1.654087e+13
Adaptive bandwidth: 41 CV score: 1.654087e+13
Adaptive bandwidth: 40 CV score: 1.651203e+13
Adaptive bandwidth: 40 CV score: 1.651203e+13
Adaptive bandwidth: 39 CV score: 1.643857e+13
Adaptive bandwidth: 39 CV score: 1.643857e+13
Adaptive bandwidth: 38 CV score: 1.635281e+13
Adaptive bandwidth: 38 CV score: 1.635281e+13
Adaptive bandwidth: 37 CV score: 1.630511e+13 Constructing the adaptive bandwidth gwr model
Now, we can calibrate the gwr-based hedonic pricing model by using adaptive bandwidth and gaussian kernel.
gwr.adaptive <- gwr.basic(formula = resale_price ~ remaininglease_years + floor_area_sqm + prx_to_hawker + prx_to_trainStn + prx_to_supermarket, data=resale_tbl.sp, bw=bw.adaptive, kernel = 'gaussian', adaptive=TRUE, longlat = FALSE)
gwr.adaptive
***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2021-11-08 01:38:11
Call:
gwr.basic(formula = resale_price ~ remaininglease_years + floor_area_sqm +
prx_to_hawker + prx_to_trainStn + prx_to_supermarket, data = resale_tbl.sp,
bw = bw.adaptive, kernel = "gaussian", adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: resale_price
Independent variables: remaininglease_years floor_area_sqm prx_to_hawker prx_to_trainStn prx_to_supermarket
Number of data points: 15901
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-197734 -72129 -21800 40093 674299
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 142448.724 13641.365 10.442 <2e-16 ***
remaininglease_years 3262.077 67.428 48.379 <2e-16 ***
floor_area_sqm 1371.204 121.416 11.293 <2e-16 ***
prx_to_hawker -68.919 1.649 -41.793 <2e-16 ***
prx_to_trainStn -47.719 2.199 -21.697 <2e-16 ***
prx_to_supermarket -45.747 5.453 -8.389 <2e-16 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 104400 on 15895 degrees of freedom
Multiple R-squared: 0.2455
Adjusted R-squared: 0.2452
F-statistic: 1034 on 5 and 15895 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 1.73102e+14
Sigma(hat): 104343.7
AIC: 412623.4
AICc: 412623.4
BIC: 396843.8
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 37 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median
Intercept -8.0380e+06 -3.3711e+05 -1.4016e+05
remaininglease_years -2.4751e+04 2.8060e+03 4.7909e+03
floor_area_sqm -6.4602e+04 1.2782e+03 2.3993e+03
prx_to_hawker -1.3557e+04 -5.8342e+01 -1.1777e+01
prx_to_trainStn -1.9680e+04 -1.1515e+02 -5.2786e+01
prx_to_supermarket -9.0354e+03 -5.7309e+01 -4.8764e+00
3rd Qu. Max.
Intercept 4.6656e+04 7205778.9
remaininglease_years 7.4232e+03 34021.4
floor_area_sqm 3.9606e+03 83281.6
prx_to_hawker 3.8928e+01 19716.8
prx_to_trainStn 7.5668e+00 8330.9
prx_to_supermarket 6.0173e+01 12804.5
************************Diagnostic information*************************
Number of data points: 15901
Effective number of parameters (2trace(S) - trace(S'S)): 1260.266
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 14640.73
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 374822.7
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 373692.7
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 366420.6
Residual sum of squares: 1.406777e+13
R-square value: 0.9386808
Adjusted R-square value: 0.9334022
***********************************************************************
Program stops at: 2021-11-08 01:39:38 The report shows that the adjusted r-square of the gwr is 0.9334022 which is significantly better than the globle multiple linear regression model of 0.2452
Visualizing the GWR output
Converting SDF into sf data.frame
To visualize the fields in SDF object, we need to convert the output into sf data.frame first:
resale_3414.adaptive <- st_as_sf(gwr.adaptive$SDF) %>%
st_transform(crs=3414)
Setting the projection:
resale_3414.adaptive.svy21 <- st_transform(resale_3414.adaptive, 3414)
resale_3414.adaptive.svy21
Simple feature collection with 15901 features and 24 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 11597.31 ymin: 28217.39 xmax: 42623.63 ymax: 48741.06
Projected CRS: SVY21 / Singapore TM
First 10 features:
Intercept remaininglease_years floor_area_sqm prx_to_hawker
1 -207463.5 6538.840 3260.5551 -64.202694
2 -255140.0 4973.831 3859.2602 -22.927203
3 -364974.2 9867.826 2702.6791 -16.894435
4 -222610.9 5450.554 2940.9428 73.955393
5 -273052.3 7778.878 2719.0350 32.513526
6 -306878.6 9811.496 2093.7020 -8.119189
7 -168062.9 9507.934 907.8766 -10.846866
8 -231862.1 6553.484 2539.4876 16.434675
9 -146064.9 7404.562 1407.6267 -48.779654
10 -195091.2 6773.747 2318.2551 -56.639485
prx_to_trainStn prx_to_supermarket y yhat residual
1 -78.48052 38.151408 330000 391939.2 -61939.207
2 -44.31763 9.179556 360000 380727.6 -20727.626
3 -93.43115 -40.205194 370000 386070.4 -16070.373
4 -21.50742 -37.747737 375000 397116.4 -22116.439
5 -72.31413 -27.129082 380000 369549.7 10450.289
6 -93.89983 -38.708983 380000 383196.5 -3196.497
7 -113.60421 -22.648319 385000 408465.2 -23465.245
8 -45.07958 -3.477971 395000 396577.3 -1577.272
9 -101.61087 36.234800 395000 392422.2 2577.759
10 -86.79003 28.585124 395000 368775.3 26224.730
CV_Score Stud_residual Intercept_SE remaininglease_years_SE
1 0 -2.07973226 73080.86 246.6561
2 0 -0.69180945 64650.37 902.8835
3 0 -0.53743763 126910.41 302.4738
4 0 -0.75838083 60359.59 615.6985
5 0 0.35517176 171040.28 503.3288
6 0 -0.10538078 113181.86 285.7373
7 0 -0.77212792 101654.55 249.4174
8 0 -0.05187776 55551.89 417.6279
9 0 0.08566000 72137.63 870.7458
10 0 0.91583702 67817.51 753.3360
floor_area_sqm_SE prx_to_hawker_SE prx_to_trainStn_SE
1 759.0503 43.48660 19.61619
2 796.8294 30.47629 17.60026
3 1263.7203 36.49889 13.84860
4 747.9891 29.67857 17.69157
5 1768.4194 43.77430 26.99447
6 1125.6782 30.63433 12.56152
7 997.1059 28.54684 12.97400
8 610.3067 24.87788 15.39005
9 757.7927 30.20387 18.93115
10 703.3059 29.37073 17.67902
prx_to_supermarket_SE Intercept_TV remaininglease_years_TV
1 50.29069 -2.838821 26.509950
2 13.04208 -3.946458 5.508829
3 36.24447 -2.875841 32.623734
4 17.59150 -3.688079 8.852634
5 36.71177 -1.596421 15.454864
6 31.18278 -2.711376 34.337465
7 24.17994 -1.653274 38.120572
8 11.21603 -4.173794 15.692159
9 13.46584 -2.024809 8.503701
10 12.99317 -2.876708 8.991668
floor_area_sqm_TV prx_to_hawker_TV prx_to_trainStn_TV
1 4.2955719 -1.4763787 -4.000803
2 4.8432703 -0.7522964 -2.518010
3 2.1386687 -0.4628753 -6.746616
4 3.9317989 2.4918789 -1.215687
5 1.5375510 0.7427537 -2.678850
6 1.8599473 -0.2650356 -7.475196
7 0.9105117 -0.3799673 -8.756301
8 4.1610025 0.6606140 -2.929138
9 1.8575354 -1.6150131 -5.367390
10 3.2962261 -1.9284333 -4.909209
prx_to_supermarket_TV Local_R2 geometry
1 0.7586177 0.8516994 POINT (29179.92 38822.08)
2 0.7038414 0.8031640 POINT (28423.42 39745.94)
3 -1.1092779 0.9663806 POINT (30550.38 39588.77)
4 -2.1457941 0.7857342 POINT (28240.06 39477.6)
5 -0.7389751 0.8751764 POINT (30443.27 38382.85)
6 -1.2413577 0.9626188 POINT (30637.92 39516.9)
7 -0.9366574 0.9474907 POINT (30347.48 38995.85)
8 -0.3100893 0.7930914 POINT (28325.75 39700.7)
9 2.6908687 0.7408476 POINT (28611.87 40270.61)
10 2.2000112 0.7757424 POINT (28271.22 40241.11)gwr.adaptive.output <- as.data.frame(gwr.adaptive$SDF)
resale_3414.adaptive <- cbind(resale_tbl.res.sf, as.matrix(gwr.adaptive.output))
glimpse(resale_3414.adaptive)
Rows: 15,901
Columns: 46
$ month <chr> "2019-01", "2019-01", "2019-01", "20~
$ town <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO ~
$ flat_type <chr> "4 ROOM", "4 ROOM", "4 ROOM", "4 ROO~
$ address <chr> "204 ANG MO KIO AVE 3", "175 ANG MO ~
$ block <chr> "204", "175", "543", "118", "411", "~
$ street_name <chr> "ANG MO KIO AVE 3", "ANG MO KIO AVE ~
$ storey_range <chr> "01 TO 03", "07 TO 09", "01 TO 03", ~
$ floor_area_sqm <dbl> 92, 91, 92, 99, 92, 92, 92, 92, 93, ~
$ flat_model <chr> "New Generation", "New Generation", ~
$ lease_commence_date <dbl> 1977, 1981, 1981, 1978, 1979, 1981, ~
$ remaining_lease <chr> "57 years", "61 years 06 months", "6~
$ remaininglease_years <dbl> 57.00, 61.50, 61.08, 58.33, 59.58, 6~
$ resale_price <dbl> 330000, 360000, 370000, 375000, 3800~
$ prx_to_hawker <dbl> 441.82653, 269.72560, 258.29513, 436~
$ prx_to_trainStn <dbl> 703.9715, 403.4297, 889.9529, 200.97~
$ prx_to_supermarket <dbl> 270.8222, 310.1889, 318.7560, 458.67~
$ log_resale_price <dbl> 12.70685, 12.79386, 12.82126, 12.834~
$ max_floor <dbl> 3, 9, 3, 6, 6, 2, 9, 6, 2, 9, 9, 9, ~
$ MLR_RES <dbl> -48105.3253, -55815.1851, -22995.642~
$ Intercept <dbl> -207463.50, -255139.95, -364974.20, ~
$ remaininglease_years.1 <dbl> 6538.840, 4973.831, 9867.826, 5450.5~
$ floor_area_sqm.1 <dbl> 3260.5551, 3859.2602, 2702.6791, 294~
$ prx_to_hawker.1 <dbl> -64.202694, -22.927203, -16.894435, ~
$ prx_to_trainStn.1 <dbl> -78.480516, -44.317628, -93.431150, ~
$ prx_to_supermarket.1 <dbl> 38.1514081, 9.1795557, -40.2051939, ~
$ y <dbl> 330000, 360000, 370000, 375000, 3800~
$ yhat <dbl> 391939.2, 380727.6, 386070.4, 397116~
$ residual <dbl> -61939.2068, -20727.6260, -16070.372~
$ CV_Score <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~
$ Stud_residual <dbl> -2.079732263, -0.691809452, -0.53743~
$ Intercept_SE <dbl> 73080.86, 64650.37, 126910.41, 60359~
$ remaininglease_years_SE <dbl> 246.6561, 902.8835, 302.4738, 615.69~
$ floor_area_sqm_SE <dbl> 759.0503, 796.8294, 1263.7203, 747.9~
$ prx_to_hawker_SE <dbl> 43.48660, 30.47629, 36.49889, 29.678~
$ prx_to_trainStn_SE <dbl> 19.61619, 17.60026, 13.84860, 17.691~
$ prx_to_supermarket_SE <dbl> 50.29069, 13.04208, 36.24447, 17.591~
$ Intercept_TV <dbl> -2.8388214, -3.9464580, -2.8758413, ~
$ remaininglease_years_TV <dbl> 26.509950, 5.508829, 32.623734, 8.85~
$ floor_area_sqm_TV <dbl> 4.2955719, 4.8432703, 2.1386687, 3.9~
$ prx_to_hawker_TV <dbl> -1.4763787, -0.7522964, -0.4628753, ~
$ prx_to_trainStn_TV <dbl> -4.0008033, -2.5180100, -6.7466157, ~
$ prx_to_supermarket_TV <dbl> 0.75861770, 0.70384137, -1.10927791,~
$ Local_R2 <dbl> 0.8516994, 0.8031640, 0.9663806, 0.7~
$ coords.x1 <dbl> 29179.92, 28423.42, 30550.38, 28240.~
$ coords.x2 <dbl> 38822.08, 39745.94, 39588.77, 39477.~
$ geometry <POINT [m]> POINT (29179.92 38822.08), POI~summary(gwr.adaptive$SDF$yhat)
Min. 1st Qu. Median Mean 3rd Qu. Max.
243002 357292 405871 433674 464960 990135 Visualising local R2
Interactive display of the point symbols on a map:
tmap_mode("view")
tm_shape(mpsz_3414)+
tm_polygons(alpha = 0.1) +
tm_shape(resale_3414.adaptive) +
tm_dots(col = "Local_R2",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
Setting back tmap mode to “plot”
tmap_mode("plot")
By URA Planning Region
tmap_mode("view")
tm_shape(mpsz_3414[mpsz_3414$REGION_N=="CENTRAL REGION", ])+
tm_polygons()+
tm_shape(resale_3414.adaptive) +
tm_bubbles(col = "Local_R2",
size = 0.15,
border.col = "gray60",
border.lwd = 1)